STUDIES TOWARDS TARGET-HORN INTEGRATION Institute of Applied Mechanics Cracow University of Technology Institute of Applied Mechanics P. Cupial, A. Wroblewski EUROnu Project

Outline of the talk 18.11. 2009 1. Dynamic response of the horn to excitation by current pulses (P.Cupial) the horn geometry – new finite-element model approximate modelling of magnetic forces response of the horn to harmonic and pulse excitation response of structures under a single pulse and a sequence of pulses – important points coupled-field approach to response under magnetic-field excitation

Outline of the talk 18.11. 2009 2. First estimates of heat transfer in the target-horn system (A.Wroblewski) horn temperature and stress distribution due to current heating early estimates of the effect of heat radiated from the target on the temperature and stresses in the horn

Horn geometry used 18.11. 2009 The advantage of studying this geometry is that the prototype is available at CERN and experimental verification is possible. Present Superbeam horn dimensions are comparable to the NF ones.

Prototype available at CERN 18.11. 2009

Finite-element model of the horn 18.11. 2009 1 X Y Z Superbeam horn FE model ELEMENTS MAT NUM 1 Superbeam horn FE model ELEMENTS MAT NUM

Approximate modelling of magnetic forces 18.11. 2009 The analsis assumes cylindrical geometry Inner cylinder with radia RI, RII and thickness t=RII-RI Outer cylinder with radia R’I, R’II and the same thickness Magnetic field distribution:

Approximate modelling of magnetic forces 18.11. 2009 Lorentz force: Definition of the pressure: Assuming uniform current density over thickness: In the case of thin cylindrical shells:

Horn response to magnetic field – FE harmonic analysis 18.11. 2009 Response at a selected point to a harmonic current with amplitude 300 kA

Horn response to a single current pulse 18.11. 2009 Response at a selected point to a current pulse of amplitude 300 kA of 100 s duration

Comments on the response under pulse excitation 18.11. 2009 Displacement and stress in the beam middle-point excited by a half-sine pulse applied at the middle point, pulse duration/period of the lowest mode = 3 The corresponding plots when pulse duration/period over lowest mode = 0.01

Comments on response under pulse excitation 18.11. 2009 Impulse resonance The case with no damping The effect of damping

Coupled magneto-structural analysis – static benchmark solution 18.11. 2009 Infinite solenoid with a circumferential current density (per area): Analytical solution: Magnetic field vector inside the cylinder: Lorentz force: Mechanical equations of equilibrium:

Coupled magneto-structural analysis – static benchmark solution 18.11. 2009 Constitutive equations: Mechanical boundary conditions:

Coupled magneto-structural analysis – static benchmark solution 18.11. 2009 Stresses in the solenoid (F.C. Moon „Magneto-solid Mechanics”, 1984): where:

FEM vs. Analytical solution 18.11. 2009 Material properties: E=10.76*1011 N/m2, =0.35, =0 Geometric properties: a=0.01 m, b=0.02 m Loading: J=106 A/m2 Results for r=0.017 m Analytical Ansys Bz = 0.003770 T Bz= 003750 T t =62.44 N/m2 t =61.34 N/m2

Thermomechanical analysis under Jule heating 18.11. 2009 Parameters used: Max. current: 300 kA Pulse repetition rate : 50 Hz Pulse length: 100 s Jule losses calculated for the NF horn at CERN by J.M. Maugain, S.Rangod, F. Voelker: 18 or 40 kW. These have been applied as uniform heat sources over the part of horn carrying the current Water flow: 82 l/min Water inlet temperature: 25 oC Water outlet temperature: 40 oC

Temperature distribution 18.11. 2009 1 MN MX X Y Z Current dissipation 18kW 25 31.093 37.186 43.279 49.372 55.466 61.559 67.652 73.745 79.838 NODAL SOLUTION STEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0 SMN =25 SMX =79.838 1 MN MX X Y Z Current dissipation 40kW 25 36.81 48.619 60.429 72.239 84.049 95.858 107.668 119.478 131.287 NODAL SOLUTION STEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0 SMN =25 SMX =131.287

Thermal stresses 18.11. 2009 1 MN MX X Y Z New HORN 03/2009, thermal static analysis 22610 .314E+08 .628E+08 .941E+08 .125E+09 .157E+09 .188E+09 .220E+09 .251E+09 .282E+09 NODAL SOLUTION STEP=1 SUB =1 TIME=1 SEQV (AVG) DMX =.001183 SMN =22610 SMX =.282E+09 1 MN MX X Y Z Current dissipation 40kW 6627 .320E+08 .639E+08 .959E+08 .128E+09 .160E+09 .192E+09 .224E+09 .256E+09 .288E+09 NODAL SOLUTION STEP=1 SUB =1 TIME=1 SEQV (AVG) DMX =.001215 SMN =6627 SMX =.288E+09 Stresses of the order of 95 MPa for the more intensive of the two heat sources. Locally high stresses due to numerical singularities.

Integration of the target inside the horn 18.11. 2009 Concept of integration of a pebble-bed target inside a horm (P. Sievers) For a 4 MW beam power dissipated in the target amounts to: 600 kW (estimated by P. Sievers) 200 kW (from the report by A.Longhin)

Horn temperature distribution under Jule heating and radiation from the target 18.11. 2009 Conservative assumption that all power dissipated in the target goes to the horn. 1 MN MX X Y Z +200kW 25 36.81 48.619 60.429 72.239 84.049 95.858 107.668 119.478 131.287 NODAL SOLUTION STEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0 SMN =25 SMX =131.287 1 MN MX X Y Z +600kW 24.964 36.777 48.591 60.405 72.219 84.032 95.846 107.66 119.474 131.287 NODAL SOLUTION STEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0 SMN =24.964 SMX =131.287 Additional heating causes a local temperature increase of 30 to 50 deg. These are preliminary results, assuming that the temperature of the cooling water is not influenced by the additional heat source (higher water flow). A FLOTRAN analysis has just started.

Plans for the near future 18.11. 2009 Continuation of the dynamic analysis of the horn under a sequence of pulses (calculation of stresses, coupled-field dynamic analysis) Transient thermomechanical analysis More detailed analysis of the thermomechanical phenomena accounting for the water flow using FLOTRAN Horn fatigue life estimate, based on the combined calculated dynamic and thermomechanical stress levels.(The present CERN estimate is only 6 weeks!) Modelling of the present superbeam geometry